What is the best way to make these wire wraps around a mesh?
I don't know if there's a "procedural" way to do it, but you could do it manually this way:


Once your body is ready, create a second mesh (plane) over the body.
Activate the Snap / Face mode, with all its options enabled.
Begin to extrude your plane to make your straps. As the Snap is enabled, the vertices will stick to the body underneath.
When you'll have finished you can add a Solidify modifier to give thickness, a Bevel modifier to make the angles round, then a Subdivision Surface modifier to smooth (+ press the Smooth Shading button on the Tools panel > Tools > Edit > Shading.
Add some edge loops to your straps to give them more angular angles.